Question

(3a^2-7xy)(3a^2+7xy)

Answer 1

$Solution,\mathrm{Expand}\:\left(3a^2-7xy\right)\left(3a^2+7xy\right):\quad 9a^4-49x^2y^2$

$Steps:$

$\left(3a^2-7xy\right)\left(3a^2+7xy\right)$

$\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}\left(a-b\right)\left(a+b\right)=a^2-b^2,\\a=3a^2,\:b=7xy,\\\left(3a^2\right)^2-\left(7xy\right)^2$

$\mathrm{Simplify}\:\left(3a^2\right)^2-\left(7xy\right)^2,\\\left(3a^2\right)^2,\\\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n,\\3^2\left(a^2\right)^2,\\\left(a^2\right)^2,\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\\a^{2\cdot \:2},\\\mathrm{Refine},\\a^4,\\3^2a^4$

$\left(7xy\right)^2,\\\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n,\\7^2x^2y^2,\\3^2a^4-7^2x^2y^2,\\\mathrm{Refine},\\9a^4-49x^2y^2$

$\mathrm{The\:Correct\:Answer\:is\:9a^4-49x^2y^2}$

$\mathrm{Hope\:This\:Helps!!!}$

$\mathrm{-Austint1414}$